In: Journal of Multivariate Analysis, 65 (1998), pp. 19-35. ISSN 0047-259X
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Abstract
Let Sigma be an unknown covariance matrix. Perturbation(in)equalities are derived for various scale-invariant functionalsof Sigma such as correlations (including partial, multiple andcanonical correlations) and others in connection with principalcomponent analysis. These results show that a particular confidenceset for Sigma; is canonical if one is interested in simultaneousconfidence bounds for these functionals. The confidence set isbased on the ratio of the extreme eigenvalues of Sigma-1 S, where S is an estimator for Sigma. Asymptotic considerations for theclassical Wishart model show that the resulting confidence boundsare substantially smaller than those obtained by inverting likelihoodratio tests.
| Document type: | Article |
|---|---|
| Journal or Publication Title: | Journal of Multivariate Analysis |
| Volume: | 65 |
| Publisher: | Academic Press |
| Place of Publication: | Orlando |
| Date Deposited: | 16 Jun 2016 07:48 |
| Date: | 1998 |
| ISSN: | 0047-259X |
| Page Range: | pp. 19-35 |
| Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
| DDC-classification: | 510 Mathematics |
| Uncontrolled Keywords: | correlation (partial, multiple, canonical), eigenspace, eigenvalue, extreme roots, Fisher's Z-transformation, nonlinear, perturbation inequality, prediction error, scatter matrix, simultaneous confidence bounds |
| Series: | Beiträge zur Statistik > Beiträge |
| Additional Information: | Arbeitstitel: Simultaneous Confidence Sets for Functions of a Scatter Matrix |
